Are you talking about the yellow badge with J-033-P on it?
Well, I think it's safe to say that if anyone has that that on the back of their Nedry badge, then it is very inaccurate, considering that that it explicitly says "visitor" on it, and these are all employee badges.
Also, I don't believe at any point do that yellow badges show up in the film. There is a piece of concept art that showcases it, which you can see on Page 12 of the Making of Jurassic Park book, directly below a concept art version of Nedry's employee badge. It may have been considered at some point, but I don't think it made it into the final film. But that is most likely how it ended up in the board game.
I would strongly suggest not using toys, games, etc. to determine the authenticity of something without a secondary source, as they use early artwork and early drafts of scripts to make their products. As a result, there are often discrepancies.
So to go back to the original point, I don't believe they should have the visitor back, as it will actually make them less accurate.